arXiv subjects

Samuel Lewis

Publications and source records attributed to Samuel Lewis.

2 recordsLinked to original sources

arXiv2025

Nakajima quiver varieties in dimension four

This paper classifies all 4d Nakajima quiver varieties through a combinatorial approach. For each such variety, we describe the symplectic leaves and minimal degenerations between them. Using the resulting Hasse diagrams and secondary hyperplane arrangements, we fully classify the quiver varieties up to isomorphism, a step in the problem of classifying all 4d conical symplectic singularities and the (2, 2) case of quiver varieties. As an application, we answer in the negative a question posed by Bellamy, Craw, Rayan, Schedler, and Weiss regarding whether the $G_4$ quotient singularity (or its projective crepant resolutions) can be realised as a quiver variety.

math.AG↗

arXiv2024

Real variations of stability on K3 categories

This paper proves that the 2-Calabi-Yau triangulated category associated with the preprojective algebra of an affine or hyperbolic graph admits many real variations of stability conditions, in the sense of Anno, Bezrukavnikov, and Mirkovi\'{c}. We do this by connecting the Coxeter arrangements of the graph with the homological algebra by introducing the concept of real flows. This categorifies the notion of above and below for alcoves in a hyperplane arrangement and allows us to generalise much of the machinery of real variations for affine arrangements to the hyperbolic setting. In the process, we show that the derived category with nilpotent cohomology is equivalent to the derived category of nilpotent modules over the preprojective algebra.

math.RT↗